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Comments

 In Italian, case only appears in the pronouns.  There are four types
 of pronouns that appear in Italian; nominative, accusative, dative and
 prepositional.  The nominative case denotes an object that is the
 subject of the sentence.  In Italian, these pronouns are io, tu, Lei,
 lei, lui, noi, voi, Loro and loro.  The accusative case denotes
 objects that are receiving the action.  These pronouns are mi, ti, La,
 la, lo, ci, vi, Le, li and le.  The dative case is used to indicate
 the recipient of an action.  The pronouns are mi, ti, Le, le, gli, ci,
 vi, Loro and loro.  The prepositional pronouns only appear in
 prepositional phrases.  They are me, te, Lei, lei, lui, noi, voi, Loro
 and loro.  However, depending on your analysis of Italian pronouns,
 the dative and accusative pronouns could actually be considered
 inflections on the verb.  In this analysis, I have decided to treat
 accusative and dative pronouns as inflections rather than separate
 words.

'objects that are receiving the action' sounds more like traditional
grammar than linguistics.  I'd go with 'object of the sentence' or
'direct object' instead.  That makes the next sentence (datives are
recipients) seem to make more sense, too :-)
 
 There are two methods of getting a noun into the accusative position
 for a verb.  It can either undergo a lexical rule that changes its
 case to an accusative case or it can be left underspecified.  If you
 leave it underspecified, it can be any case.  This is a problem, since
 nouns can never be dative.  Only pronouns and prepositional phrases
 can fulfill a dative argument on the verb.  However, in this
 representation, dative pronouns are considered inflections, so in the
 end nothing is considered dative.  Verb can be marked as only allowing
 prepositional phrases to fulfill its dative argument, and lexical
 rules can add the required inflection while fulfilling its requirement
 for a prepositional phrase.  Since there no longer is a dative case,
 nouns can be left underspecified and can take on any case without
 worrying about accidentally becoming dative.  This is done even though
 traditional Italian grammaticians have always placed dative as a case
 in Italian.

Your way makes sense to me.  Note: traditional grammarians, not grammaticians.

 Italian nouns agree with their determiners and adjectival modifiers in
 number and gender.  There are three genders in Italian masculine,
 feminine and (I just barely learned this) neuter.  Gender acts like
 noun classes, but has loose connections with actual gender.  Most male
 people are masculine, and most female people are feminine.  There are
 exceptions.  For example, all pilots are masculine, and all people are
 feminine (even a group of males).  Other than that, gender acts mostly
 as an arbitrary noun class to which things are assigned.  Neuter
 objects are rare.  There are only traces of neuter in Italian,
 remnants of its Latin heritage, being mostly contained with the body
 parts.  Neuter objects act like male objects in the singular, but
 feminine objects in the plural.

Romanian has a similar residual neuter --- you might discuss this
with Jonah.

 Note that it is not the subject that is agreeing with the verb, but
 the verb that is agreeing with the subject. 

Right --- that is what we mean by subject-verb agreement.

 The three verb types inherit from the verb-lex.  I created a new ALTS
 value, called VERB-CLASS that stored the type of verb it was.  Since
 many of the conjugations of `ere' and `ire' verbs are
 actually the same, I put them together in a subtype. There are two
 direct children of the type verb-class – `are' and
 `non-are'.  `non-are' in turn had two children,
 `ere' and `ire' verbs. 

Nice.